How Does a Rocket Behave After Engine Shutdown?

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The rocket, launched with an initial velocity of 80 m/s and an acceleration of 4 m/s², reaches an altitude of 1000 m in 10 seconds, achieving a final velocity of 120 m/s at that point. After engine shutdown, the rocket enters free fall with a gravitational acceleration of -9.8 m/s². It continues to ascend briefly due to its velocity before starting to descend. The discussion highlights the need to calculate the distance traveled during free fall until it comes to a complete stop. Understanding these dynamics is crucial for predicting the rocket's behavior post-engine shutdown.
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A rocket is fired vertically upwards with an initial velocity of 80 m/s with an acceleration of 4 m/ss until it reaches an altitude of 1000m. At that point it goes into free fall (a= -9.8)

What time interval is the rocket in the air?
What is its maximum altitude?
What is its velocity right before it hits the ground?


Does this mean that the rocket continues to go upwards after the engine fails?

I got the time until that point to be 10 seconds and the final velocity a that point (1000m) to be 120 m/s. Afterward, all I can come up with is a initial velocity of 120 m/s and gravitational acceleration. I can't find t without another variable.

Thanks in advance
 
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You need to calculate the distance the rocket travels after the engine fails before it comes to a complete stop.
 
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